Many of our present technologies use signal processing principles to achieve their communication functions. In a typical signal detection application, the receiver performs the function of receiving and processing signals. A design engineer using a receiver to perform signal detection designs the receiver so that it is capable of receiving and processing a predetermined set of signals. These signals vary depending upon the system in which the design engineer is deploying the receiver. Because signals received after transmission typically contain a noise component, the receiver must process the received signal and extract information regarding the transmitted signal. The receiver may contain a detector or similar device, which could be used to determine which signal within the predetermined set of signals was in fact received by the receiver.
Many prior art receivers perform signal detection by using a correlation demodulator and a detector. One example of a correlation demodulator is a matched filter demodulator. A single matched filter is basically a linear filter whose transfer function has been matched to a particular electronic signal or environment in order to perform a filtering that is optimum for some particular purpose. See generally U.S. Pat. No. 4,044,241 “Adaptive Matched Filter,” the contents of which are hereby incorporated by reference. The filter is particularly matched to a signal plus noise input from which the signal is desired to be extracted. Id. A matched filter demodulator is comprised of a bank of matched filters the output of which is sampled at one time instant to obtain a vector signal.
The matched filter demodulator can equivalently be implemented as a correlation demodulator with correlating signals equal to the time-reversed versions of the filters' transfer functions.
When one of a predetermined set of signals is received in additive white Gaussian noise, the matched filter detector is optimal for maximizing the probability of detection.
The matched filter detector is comprised of a correlation demodulator, where the correlating signals are equal to the predetermined set of signals that could have been received, followed by a detector. The detector declares as the detected signal the one for which the output of the correlator is a maximum. See generally J. G. Proakis, Digital Communications, McGraw-Hill, Inc. 3rd ed 1995, the contents of which are hereby incorporated by reference.
Although matched filter receivers are optimal when the added noise is white and Gaussian, they are not when the received signal contains added non-Gaussian noise, or other forms of distortion. Design engineers nonetheless continue to use matched filter receivers in operating environments containing non-Gaussian or non-additive noise, in part because optimal receivers for these noise environments are typically nonlinear and, therefore, difficult to implement. Furthermore, in many applications the noise distribution is unknown to the receiver. See generally T. Kailath and V. Poor, Detection of Stochastic Processes, IEEE Transactions on Information Theory, vol. 44, pp. 2230-59, October 1998, the contents of which are hereby incorporated by reference. In light of the fact that many receivers are required to perform in situations where the added noise is non-Gaussian or a combination of Gaussian and non-Gaussian, there is a need for a receiver which is simple to implement, does not rely on the channel parameters and can achieve an acceptable probability of detecting the correctly received signal irrespective of whether the noise added to the received signal is white, Gaussian, or non-Gaussian.